Droid lags and some apps wont run when charging

I'm very new to smartphones so I don't know what to expect. I was browsing the app store on my phone when it told me it was low on battery... so I plugged it in and tried to run the recently downloaded app when it started lagging, I couldn't open any apps and the phone was acting up, like misclicking. help please, thanks

EDIT: when the phone is plugged in, it goes crazy when I try to touch icons, it stops when I unplug it. Is this normal or did I buy a defective phone? I don't have a SD card in it, could that be the problem while charging?